 Good morning No, that's awesome and happy spring. It's supposed to be spring today at least Let's see first things first Lecture notes for today. I'll pass them around So after last week we had three intense lectures getting everything started this week We're gonna continue with first a little bit more about biology today Just to make sure that all of you don't run away after the physics tomorrow We are gonna do some proper physics and derive the Boltzmann distribution and some related stuff in the general case And then on Wednesday before Easter I'm finally gonna get to real proteins and then I'm gonna bring up a little bit What would you do when you need to do either a simulation or a model or something of an actual protein? And what is that we need to think of and as you're gonna turn out then it's Fundamentally, it's not really anything different. It's a whole lot more detail And that's why we started with the simplified cases first As some slash most hopefully all of you might have noticed I finally had some time yesterday afternoon and created a new website in canvas Which is so not an official tool of Stockholm University But I kind of like canvas and I've thought about doing it for years So I'm a little bit sorry that you're gonna be guinea pigs for this new website I'll make sure that all the material is available on the old website for to if you absolutely love Mondo and feel that you so want to submit all your assignments there go right ahead and do it we will handle it But personally I fell in love with canvas roughly 10 minutes after I started editing it It's like five times faster for me to add stuff there and we might even We might even do some trials with some quizzes and assignments for you not because it's gonna count towards grades But it could be Well, if nothing else it could be good formative assessments You have a chance to click through things and feel that do I know the stuff we covered the first two weeks? But since I haven't done it yet. No promises. It depends how easy it is for me to do And while I'm at it there, did every did all of you get that email I sent yesterday? Okay, good. See if you can sign up with canvas if it if you can't get into either website It's important for me to know if you can't get into canvas. That's probably easier for you But otherwise we'll take it as in cops I also noticed that we had made an error and Dari I think had by mistake said that today was the deadline for lab One I said one week. So you have one week so that the deadline to add in reports for the first lab It's going to be Thursday like one minute to midnight And I'm a bit hesitant about that one week because the whole idea with these lab reports is that they're going to be short Dari and Björn and I we just want to know that did you understand the concepts and did you follow it? Because if you did not follow it well first I'm gonna need to cover it in better detail here and they will have to explain it better to you in Principle if you spend one or at most two hours after the lab you couldn't theory upload that the same night you did the lab So the problem with giving you one week is that I'm a little bit worried that some of you will take that Oh, I'm gonna wait six and a half days before I start don't do that spend one hour right after the lab And you're gonna be all in sync and I would particularly recommend that this week because let's see Wednesday Today this morning we have lecture stuff and then after lunch We're gonna have a lab and then tomorrow you can have another lecture that leaves Tuesday afternoon to fill in lab report if you absolutely don't want to work evenings And then a Wednesday we have lecture and lab again, but then on Thursday you get an early Easter break If you fill in everything so if I were you I would fill in lab two and three on Thursday evening Sorry, Wednesday evening and be done with it. And then you don't have to think about the University until April 2nd. Yes Yes You have you have so the second lab is already up there, but the second lab and I think all the material for lab three is on the old Mondo site Daria is gonna move that to the other side So you're more than welcome to do the labs at your own pace if you've already finished the lab I think in particular if you're doing it early Daria Byrne will likely be more than happy to help you there, too But you can do all the labs at your own pace if you want to and I think the only updates They do is that they they improve things and they realize some things might all have been clear since last year and everything But in principle the lab material is the same as last year and all that stuff is already available in Mondo Good. So that leaves today's lecture Secondary structure and amino acid properties. I'm well aware that this sounds like stuff You already know but what I'm gonna try to go through it's a little bit more detail And now I'm also gonna try to connect this back to free energies in particular and discuss why things happened And you're gonna hopefully we're gonna continue the slavery But before we do that we are gonna spend some 40 minutes or so with discussion questions Let's see if this works. We have all of you participating. Otherwise, I'm gonna start going through the entire room again So what's the difference between Helmholtz and Gibbs free energies since you're in practice? Fun Monday morning exercises, right? Yeah, you could say that's semi implying well that you know that that is the theoretical difference But what does that theoretical difference correspond to? You have it, but it's just the formulation The reason why these formulations are important is that it's related to the concept of ensembles in physics So if you think of the entire system, what does the pressure and volume correspond to? Sorry Yeah, well You change the energy to the enthalpy but this primarily has to do with whether the system Exchanges mechanical work with the surrounding Whether the surrounding is doing mechanical work on the system or whether the system is doing mechanical work on the surrounding a Mechanical work might sound a bit abstract But that's every time you have a test tube and the volume in the test tube changes You are actually exerting a bit of work on the air So the opposite of that would be a system that only can exchange heat a so-called adiabatic process That's not part of this course. And if you can only exchange heat the pressure and volume well Pressure multiplied by the difference in volume is always going to be zero if there is no difference in volume, right? And that's also when so if it's an adiabatic system that only exchanges heat with the surrounding Then we use the Helmholtz free energy And then you're quite right in the case where we can exchange also can do work or the Surrounding does work on us with up with the Gibbs free end So if your chemist here, which one is the most relevant for you? Why? Exile well Yes, exactly that test tubes or everything we do right cells and everything we do not keep the volume constant Even you might think the volume is constant. It's not strictly constant adding one milligram of protein to a cubic meter of water Technically changes the volume just a little bit And now I kind of spill the beans with the practice thing to that for most things related to proteins in particular The changes in volume are so minute that it doesn't matter But mark my words there key most cases proteins If you're mixing one liter of ethanol with one liter of water You end up with roughly 1.8 liters of volume and In that case, it's a horrible approximation to assume that the volume was constant in the process So it's not true for chemistry in general, but it is true for protein-based chemistry And what that means in practice is that we do this horrible thing that we call it the Gibbs free energy We call it Delta G and We call it enthalpy, but we never really I don't I can't remember it now But I don't think we ever include the PV term in any lecture in this course It might be part of the simulations and that's also why we use Delta G don't and then H You can say that H for the H in enthalpy is occasionally for Helmholtz But the point is that all these letters and everything there is no good standard for it So that just make sure if you're using the default letters You don't necessarily have to explain what it is if you have the slightest doubt whether you're using the right letter Define what it is. You're more than welcome to define anything you want alright Number two give some examples of relevant versus irrelevant energy barriers at room temperature You could probably interpret this question in two ways Let's take a step back then Why do I even ask this question? Why are they relevant versus irrelevant energy barriers? Yes, but why do we ask that question? What decides whether the barriers are relevant or not Yes, and in particular KT in the Boltzmann distribution, right that the probability of something happening is Proportional e divided to Delta G divided by KT So depending on the value of Delta G here, we're gonna end up with probabilities that are either almost zero or Well, very close to one or they're gonna be well some sort of intermediate range when We might sometimes be able to pass it and sometimes not So if the probability is virtually zero here That's a barrier that's so large that you will never be able to cross it and that happens if Delta G is much larger than KT If Delta G is much smaller than KT the probability is gonna go to one so you could argue that What I meant that there are two ways of interpreting this as Obviously if the barrier is so much smaller than KT that you can always get over it. It's not really a relevant barrier But you could actually say if the barrier is much larger than KT Well, it's obviously relevant as a barrier, but the exact height of the barrier is not really important, right? Assuming if you're doing high jump and you're gonna jump over a bar. That's 10 meters or 50 meters high It doesn't really matter because I can't jump over it in any way But whether it's one meter or 1.5 meter is probably irrelevant to me because well I used to be able to do 1.5 meters in high jump when I was 20. I certainly can't do it now and That's goes back to knowing your energy barriers and KT Let's see. Do we ask about KT here? No, we don't so let's ask about that again. What is KT? Per mole and how many kilojoles? Sorry 2.5 No for your sake, no both values because otherwise you're gonna constantly gonna need to translate So what are some relevant versus irrelevant barriers? Particularly in the case of proteins perhaps a torsion angle is what? It's relevant And that indirectly means that it has to be roughly in the same a few KTs or something so it may be Maybe two to five kilojoles a kilo-cals per mole or so That's might even a bit high, but so that there are some torsion barriers We can't cross and others we can't cross and that means that we have to care about them all the time So can you come up with some other barrier that is relevant? Let's start with another barrier that is relevant Yes, what but what barrier are you talking about them? An example of a process that might have something in that ballpark I'll give you a clue something in water Hydrogen bonds few K-cals maybe five maybe ten K-cals We're gonna we're gonna come back and talk more about hydrogen bonds But again, I don't really care about the factors of two because that will depend on the surrounding But the point is it's not one K-cal and it's not 50 K-cals So hydrogen bonds are going to be important to and that's why we keep harassing you with them, right? They're going to be so many cases where whether a hydrogen bond is formed or not will be important and both possibility both cases are possible So can we think of some other barriers that are not usually not that relevant either because they're too high or Extremely low because it is It is high so that that doesn't mean we can ignore electrostatics, right? But we usually can't get over an electrostatic barrier if you're talking about something that's 100 kilo joules per mole or 100 K-cals per mole Even you're never gonna take two positive charges and push them through each other Same thing there if you have one positive and one negative charge as a salt bridge That's gonna be so strong that the likelihood that you can just break that. It's almost never gonna happen With some caveats that I will come back when we talk when we talk about proteins Lena-Jones interactions, what do you know about those? So what is the strength of an individual Lena-Jones interaction the dispersion in particular? It's extremely weak right that the repulsion part gets strong So you can't push atoms on top of each other, but an individual Lena-Jones attraction If you don't know the numbers you think about things that for instance The reason this attraction is the reason why even noble gases eventually condense and that's going to be at minus 270 Kelvin or something by definition that has to be extremely weak on the other end at some point You have lots of them right and that adds up but an individual Lena-Jones interaction is exceptionally weak and This is another example of a strong one is a bond So you're not gonna break bonds in proteins because they're so exceptionally strong Even angles They vibrate a bit, but in principle angles are not particularly important. They might vary between 115 and 125 degrees But you're never gonna get taken angle and move it to 180 degrees. The energy would cost too much So this is really the reason why we focus so much on the torsions the Ramachandran diagrams When we talk about Leventhal's paradox the torsion degrees of freedoms are the most important ones in proteins because they just happen at Room temperature, they just happen to be in the right ballpark where they are relevant We can occasionally cross them and we can occasionally we can't cross them How can you predict what processes will occur? Yes So sorry say that again Fundamental yes, so that is the Lena-Jones interactions. I Will come back to that. I think on Wednesday So that's it's enough for you. Well fortunate or unfortunate case when we use many different terms for the same thing Fundamental interactions is in general all weak non-electrostatic interactions between atoms and part of this has to do with the repulsion at short range and part of it has to do with the attraction at long range and Then there are of course different ways. How do we describe the repulsion and how do we describe the attraction? And one specific form of describing this would be the Lenard-Jones interactions So you can think of the same thing as Electrostatic interactions are all the interactions, right? Coulomb's law is one way of describing them So I would and again, this is a bit fussy, but normally I would say when you say Lenard-Jones This is the way of describing Funda-Wall's interactions But one over R to the power of 12th term for the repulsion and one over R to the power of 6th term for the dispersion But that people violate that all the time, but so Lenard-Jones and Funda-Wall's is roughly the same I'll explain on Wednesday why we use the one over R 12th term So the the the caveat here is that it depends on what to say so that the repulsion is obviously irrelevant, right? You can't get atoms to overlap the weak dispersion interactions if you look at one of them It's going to be very weak So then you can cross it all the time on the other hand if they add up at some point they all start to become important so I would It's a bit of a caveat with this question that you have to describe what you mean I would say when they say relevant irrelevant barriers if they're too low They're definitely irrelevant and if they are too high it definitely presents themselves as a barrier So it's up to you. How do you interpret the question? You could argue that there are kind of three ways you want to classify barriers significantly lower than KT Significantly higher than KT or say within five order was within a factor five of KT Because I would actually the most important ones are the ones that are within a factor five of KT Now of course if you're doing things at 100 Kelvin KT is different and at 3,000 Kelvin KT is also different So how can you predict what processes occur? Well, yes and no that's probability of individual states or even microstates Intimately related to that but not quite the free energy and in particular the difference in free energy and When do processes happen when the difference is negative? Yes Now how fast do these processes happen on the other hand? That's not the first thing this link if you didn't follow it what this link goes through it actually It exposes that this free energy is the energy available to do work. It's not a super complicated derivation and If you have this strange if you have this awkward gut feeling that you don't really understand what free why is it called as free energy? Follow that link. It's not a very difficult derivation And that really shows you that the free energy is going to correspond to the energy available to do mechanical work And that's why we call it free energy Now if I show you two processes one of them, let's see here's where I start And one of them goes like that If that is a and that is B if I start out that a You probably agree that we're pretty quickly gonna end up in B, right? If this is some sort of Delta G on the other hand if we start in a And if it looks like that Are you gonna end up in B? Well, it's gonna depend on that barrier, right? We'll come back to that later. So in some case if the barrier is very low We will go over it and in some cases the barrier is very high. It might take a very long time So all the free energy says is that in principle it is better to be there, but that For it happens spontaneously. It has to be a straight downhill process So this case we would need to start to go uphill which we can sometimes do but not always But if it's a straight path down, we're always gonna go downhill in free and don't worry I'm gonna come back to that when we talk about kinetics So what is the difference between hydrogen bonds in vacuum or versus water? In particular think if it's protein or something as you probably noticed these discussions questions are not quite as easy as they were It's the very first lecture, right? So this is part of my reason for doing this to if you feel that it's difficult to follow these Try to look at the lecture in extra time or go through the lecture notes or something There's that I'm well aware that we're pushing your heart and everything but The more you keep up with the lectures. These is gonna be for you. So let's Anytime you have a question with difference think of one case and then the other case. What is different between them? So what happens when you're for yes? So that yes, so that the difference is in vacuum. Of course, it's a net positive, right? Without before you have a specific hydrogen bond saying the protein formed you don't have the energy of a hydrogen bond And when you form it you have the energy of a hydrogen bond So that means it's clearly a drop in energy, which is good And then there are some entropic effects, but they're not going to be quite as strong If you're having a protein in water on the other hand when you first have the protein extended and then the protein folded up and forming hydrogen bonds As you mentioned there isn't really a net difference because when the protein is stretched out all the parts of the protein will be making hydrogen bonds to water and Then when you fold up the protein there isn't really any net change in the hydrogen bonds But suddenly you have the protein forming hydrogen bonds inside the protein and The waters that previously formed hydrogen bonds with the protein. They know form hydrogen bonds with each other instead So that the net difference in energy is going to be very close to zero And in that case the whole difference is rather going to come from the entropy, which is likely a much smaller difference But we're going to come back to that too So what are partition coefficients and why are they useful even for protein folding? So partition coefficients was this feature that all of you had used but you might not have called them partition coefficients Is that formula right? So you're inverting the Boltzmann distribution So K here is some sort of constant of an equation of a rate equation or something That tells you how likely is the how what concentration are you going to have on the right-hand side versus the left-hand side That's going to tell you how much product you have versus the components or For instance, how much of a particular molecule are you going to have solvated in oil versus solvated in water? So that the second, you know a relationship in concentration or spectroscopy Absorbents or something between two you can tell how much do I have in state B versus how much I do I have in state A and The reason why that is equal to Delta G whether they say RT or KT here doesn't really matter It's just better. We calculate cancel mole that is because the K is proportional to e to the minus Delta G in this case I'm going to have said divided by RT because I'm measuring a mole, so I'm literally just taking the logarithm of both sides here and Well the proportionality here is going to end up being a constant and if it's a Delta G I don't really care about the constant So you're inverting the Boltzmann distribution and by inverting the Boltzmann distribution I take this it turns out that the part on the left-hand side you can usually measure from the lab, right and Then I can use that to get the difference in free energy between two states And you use this all the time because measuring things in the lab in is easy Calculating Delta G is usually very hard and in particular for protein folding the reason why we do this is that this way We can calculate for instance the solubility in how much does it cost or how much do you gain in kilo-cals per mole to solve a say different small molecules a ethane Toluene benzene and while this is just small chemical molecules they correspond exactly to various side chains in amino acids And that this is going to mean that we know roughly how much it will cost to Transfer different amino acids between water and oil or air to water Which as we're going to see today, I think It's very much related to what secondary structures they were for Six why are free energies so intimately coupled to experiments it touches upon two of the previous ones? Yes, they describe what happens in the lab, right and that is the difference energy on the other hand does not The energy will not always go down in a reaction You can have a but there are a bunch of reactions where actually the energy goes up But the free energy goes down and they will still happen So energy is not a good way to measuring what things will happen versus not But the free energy will always decide is some are you gonna observe something any time you observe something happening? It's because there was a favorable change in free and so that leads to the next question, but what if you take? For instance water will water spontaneously boil It won't right, but you can take a bounce and burner and boil water So apparently I can have a process where there is a positive change in free energy Does that mean that free energy is not correct? Exactly, and I'm burning propane or something right so in the universe as some you have to expand your system And at some point you have the entire universe and in the entire universe the change will always go down in free energy So the only reason why the water boils is because I'm burning propane and the burning the propane reduces the free energy more Then I use it to boil the water. Ah number seven. What is temperature? That is an example of a derivation I might ask you to do at some point I'm not gonna do that particular one because that I and I did here, but Mainly because I can tell you start from this equation and work your way through it So temperature had to do with how much the number of available states i.e. entropy Changes as the energy goes up It's exactly it's the derivative I'm gonna talk more about that tomorrow, and I know this sounds super strange and abstract to you now It will hopefully be a bit more concrete tomorrow when we look at some plots But the point is at this point. This is just a definition and so I'm not sure whether I should be enthusiastic or Sad here has each of you remember before you started this course You thought temperature was easy and entropy was difficult and now your old question marks when I ask you about temperature At least you've understood that temperature is complicated Or rather it's actually not complicated, but the whole point. It's something we can define. It's a very easy property to measure and We can simply measure it from this derivative of how the number of available state increases as the energy increases Which happens to correspond to how hot we feel things are so how does the hydrophobic effect vary with temperature We had a plot or two about that last time if you had the lecture notes, you can even look it up This is this plot that says temperature dependence So why is this important in the first place as you will find out in chemistry. There are lots of Measurements and everything that people do as either as a function of temperature Well primarily as a function of temperature and the main reason you want to do it as a function of temperature Is that it can help you understand what type of process it is? Which is pretty amazing because now we talk about doing things in the lab with a Bonson burner and a thermometer and then just Measuring things you have absolutely no atomic detail whatsoever in the experiments and you don't need any fancy equipment But that can help you understand something very very deep about the molecular properties of the involved atoms and interactions The most chemical process is what happens when you raise the temperature Say if you're solvating a salt and water or something Faster and easier and you increase the solubility of a salt if you look at this diagram What happens with the hydrophobic effect when you raise the temperature? So how many of you have ever you you've probably done some very advanced Biophysical experiments in your kitchen at some point. Have you ever boiled pasta and what you typically have in the water when you're boiling pasta? and Maybe a bit of oil So what happens with the oil when you boil the water does oil suddenly? Partition all over the water You can't solve it the oil just by raising the temperature, right? So it actually turns out the hydrophobic effect becomes worse more pronounced when you raise the temperature So the solubility of oil actually goes down as the temperature goes up And the second you hear that something becomes more pronounced at high temperature You should be able to say something based on the equations, we know and if I if you have no idea what equation I'm talking about take a guess good If you have no idea what equation you should use it's probably 50-50 that is this one and if again There will be temperature variations of all these terms and everything But the strongest variation is usually going to be the one that has the t explicitly and it's right The higher the temperature is the more the second part of this equation is going to matter the stronger this one will be So if a process is very sensitive to temperature, it's likely what type of process? Exactly the free energy of the barrier so that it's going to be dominated by the entropy While on the other hand solving the salt is likely a process dominated by The enthalpy because it's less temperature dependent. This is pretty cool, right? You don't need a microscope You don't need a fancy x-ray solution and you and this is how we've been able to say that hydrogen bonds are in tropic You don't need any molecular detail. You certainly don't need computer simulations to say it all you need is paper pen You don't even need to do the experiment yourself because people have done hundreds of these experiments already use somebody else's experiment Look at the curve and think about it And this is why these equations are way more powerful than you think That's actually particularly why I like it because they're powerful Not despite of but because of their simplicity if this was an equation with 500 terms You needed to do a computer simulation Then we would also need to worry about our approximations, right? But there aren't really any approximations in these equations they're universal because they don't describe the details of a system They describe general properties So the hydrophobic effect is the effect why oil is not soluble in water Yes, but if you look at that thought it becomes it does become better It becomes harder to solve to solvate oily water as the temperature goes up That is an experimental result. It's not something you can deduce But because of that experimental result we can deduce that it's dominated by entropy So that has to do with well, yes and no So all we can say is that it's in tropic. That's the only thing we can say from the lab exactly why it is in tropic There i'm for now hand waving But that had to do with the effect that the hydrogen bonds are so strong Actually, we'll come back to that at question 13. So wait, hold on a second But question nine is also related to it. Why is the hydrophobic delta g so well correlated with a non-polar surface area of a molecule? Do you want to try answer it? Yes, I know from one point of view This is a horrible approximation, right because it's not like you're forming hydrogen bonds with the surface area It's not that we can form hydrogen bonds with any atom But this is an example that simple approximations usually work quite well So on average it turns out that the hydrophobic effect is going to correspond It's going to be almost exactly proportional to the non-polar surface area Which again because that's roughly the amount of hydrogen bonds you could form Rough as a keyword. There are some deviations from it, but they're surprisingly small That's the other lesson here. Don't try to create an advanced model before you try the simple one Always start with the simplest possible model if that one explains your phenomena There is no there are no brownie points for having a more advanced model It will just make it more difficult for you to understand the model But the answer to that question of course starts to bring us a bit closer to what you asked for the model What happens on the molecular scale? There is something here that is proportional to the surface area So now we know that it's not just entropic that we knew from the temperature behavior We also know that it's somehow proportional to the area at least the hydrophobic part of the area of the molecule So somehow it's going to have to do with the interface between the water and the molecule We're not quite at what you wanted yet, but that will come at question 30 Actually, let's take question 13 right now So you don't forget it. So there I ask the book even says that The electrostatics in water originates This electrostatics You might even say I would even say hydrogen bonds So the way I put that this is a bit of a paradox that the hydrogen bonds in water They're of course explained by electrostatics But the hydrogen bonds are entropic in nature Rather than entropic So why do we say that? And that has to do with the molecular explanation to the hydrophobic effect So if it's complicated again, let's separate it into multiple parts Why is there no net change in energy if you solvate some sort small hydrophobic molecule in water Shouldn't we break lots of hydrogen bonds? Right or the electrostatic interactions are strong that had to do with these barriers I spoke about right we do not want to break hydrogen bonds because it would cost too much And because you don't want to break hydrogen bonds, we will have to maintain them one way or another at any cost So that brings us to the first part. We don't break hydrogen bonds. We maintain hydrogen bonds Does that solve the problem? So what's the second part of the problem with what I said It's the how right how do you maintain the hydrogen bonds because we obviously no longer have the partners in the protein Or the molecule the part that would be used to be able to form hydrogen bonds now. There is a piece of a drop of oil there So how do the water molecules maintain the hydrogen bonds? Exactly, they will need to reorient around this molecule and form hydrogen bonds Basically, if you think of this as the floor, I can form it to the top left right forward and backward But I can no longer form hydrogen bond downwards because they're where I have my hydrophobic solute This is a more ordered state because I can't form hydrogen bonds in all directions, right? And because it is a more ordered state as you say, we can even talk about this as a cage like clathrate structure But by definition, if it's more ordered that will do what? Exactly and lowering the entropy is good or bad bad And that means that it's going to be a rise in free energy and that's why it costs free energy to solve the hydrophobic compulsive water And somewhere here we start getting very Then things start to become very difficult because these clathrate structures. There are some experimental examples of it But then the frequency has to be based on very fast lasers spectroscopy or something because they're they're not rigid They're not a crystal structure So knowing the structures of these clathrates that's research that people have done the last 20 years or so But so but all the way getting to the point that understanding that somehow the waters must be more ordered That we can get with reasoning but exactly what the structures look like we need very advanced experiments or computer simulations So let's jump back So what is what is the role of epsilon or let's start with what is the matrix or epsilon? Yeah, so they we even call it the dielectric coefficient And this is very important then say condensers or batteries or anything and a high value of epsilon means that You can either talk about this in absolute terms So what we frequently do is we talk about epsilon r the relative one that is What is the factor compared to the permittivity or the electric coefficient of free space or vacuum even air is very close to vacuum And what is this for water the relative one? Roughly 80 So in principle water would actually be great to say using condensers or something And occasionally we actually have wet condensers not so much for the waters, but with salt and other things It's just that you don't want it to be Conductive because it's conductive the ions would slip right through So why is the wall value in water so extremely high? movable in what way and how Except the point that the whole water molecule can flip around And if I ask you to make some predictions here, what would happen at very low temperature? Would epsilon be roughly the same or would it go up or would it go down? Why and at some point you form crystals, right? So water and crystals is not as movable as it is in free water Same thing if you go up a lot in frequency Which is not really that relevant in biophysics, but this is the way we can measure where it comes from At some point the frequency is so high that the water doesn't have time to move with the electric field And then epsilon will go down too Ah, sorry. I just asked a question 11. My bad So what is then epsilon roughly inside a protein? Sorry Why is it three? Why is it not five? The point is it can be five to right. It can probably even be upwards not 10 is a bit high, but The point point is that it's significantly lower than water And it's always going to be above two I would say and that's because you always have electrons and the second You have electrons They are a bit polarizable And the reason why it's so much lower than water. Sorry you might have answered that, but I didn't listen Well, remember so why is it so high for water? The entire water molecules can rotate, right? So the entire dipoles can flip around Could you imagine that happening inside a protein? One well there might be one or two hydrogen bonds that can but in general You can't take the peptide bonds and flip them around 180 degrees because the protein is packed and What does that imply for the electrostatic interactions in proteins? Are they stronger or weaker? They will have a much larger effect, right because you don't screen them And that's why it's It's not just the fact that it's not really ideal to have an unpaired ion in water either But in water first, it's heavily screened that it will interact all the waters will turn its oxygen Against that unpaired ion Inside a protein having an unpaired charge. It's horribly bad from a free energy point of view And if you now compare this unpaired charge, should you have it in the protein or should you have it in water? It's better to have it in water, right And that will lead to this type of hydrophobic effect that Charges in particular virtually never occur inside proteins because it's so bad Which relates us to question 14 then what would happen if anyway if I force a titrate What is a titrate ablamino acid in the first place? Yeah And in principle, there are there are lots of amino acids where this could theoretically be the case In practice, this is roughly identical to the ones we typically call charged Because unless you're moving to completely extreme pH values, we will look a little bit about that today But what would usually happen if I force say a Glutamic acid to be on the inside of a protein In water, it would be charged negatively charged They would typically be protonated, right? So when it's protonated, can you then have it on the inside of a protein? And that does means that it's going to be good and everything and it's not really bad to have glutamates inside a protein because it can be protonated So why is it bad? Well, it's not charged, right because now it's neutral Or because free energy, right? It's you're going to pay a lot in free energy to protonate the glutamate So that there is no way around this the only question Do I pay it by paying free lots of free energy for having a charge on the inside of a protein? Or do I pay a lot of energy for changing its protonation state? So it will never be good, but it's if you absolutely need to put it on the inside of a protein It might be slightly cheaper to protonate it or deprotonate it first, but it will never be good good Lots of stuff there What we're going to talk about today Is that we're going to move from that super simple case to the real stuff proteins And in particular understand how hydrogen bonds and entropy and enthalpy gives rise to the secondary structure But before I do that, I'm going to spend just a few minutes on something else In most of these courses we talk a lot about modern science and we Virtually only talk about things that are right That's actually why we deliberately included some things for instance the line is pulling dna structure and everything that were wrong because it also I think it's important because it helps you understand how science works So I had I had dinner with my father on Thursday in lund his retired professor and medical microbiology and even We started talking about this and then I brought up this paper in the course and even measure That's at some point in an interview a few years ago Jim Watson had even said that Remember how I said that Pauline produced these incorrect structures, right? Uh and Jim Watson at some point said well if line is pulling had just come by Cambridge and ask us We would have given him all the data and then he would likely have solved the structure but Whether that is a rumor whether it's mostly Jim Watson that is related to the fact that Scientists were often too proud starburn and everything To accept that other people might be pretty smart too or accept that may right be wrong and that's dangerous because Incorrect things frequently keep either you publish a paper. That's incorrect or incorrect assumptions tend to live way too long in science And that is partly related to some other things. I'm going to show you So in the 1960s some of you might have read this already in the 1960s. There was an amazing result And this is actually a real picture from the natural bureau of standards in the u.s. Let's see A small example in a test tube that in Russia. There were a couple of Scientists and in particular this was confirmed by the ryagin. It was pretty much the most famous scientist in Russia That uh fed yakin had first observed that under some very special conditions If you put water through very very very thin capillaries this water could somehow spontaneously condense And form a face with very special properties. You would have a viscosity that is 10 times higher And a completely different spectroscopic properties and everything And they gave this new face of water a new name called poly water. So basically the water would polymerize And this is a Real example from a paper by lippencott from the u.s. Where they too the u.s. Were able to reproduce this a few years later Uh And they argued that you see all the small water molecules here, right? And then they would argue they would form somehow form an extended network of hydrogen bonds Which doesn't really correspond to ice But it's a much more rigid hydrogen bond network that you would expect under normal circumstances And this went so far that They were even able to determine quite a lot of properties of this water that you would have a freezing point Roughly around 200 Kelvin plus and a boiling point at 500 Kelvin And the u.s. Were so worried about this that they argued that russia was on the verge of developing a poly water gap Because new amazing properties I would guess that you haven't read this in your undergraduate physics textbooks, right? And this of course because it's wrong. It's completely wrong What is wrong with this? You can explain this and they should have been able to find out Richard Feynman actually explained this a few years later with the typical very very simple reasoning So of course it's not completely obvious, right? But what I'm going to let's do one of these peer exercises again So talk to the person right next to you and try to understand Can we with based on what we know? And in particular that curve How the free energy of areas of the three different phases explain why this can't be true Take a minute and I might give you a lead if you want Not entirely easy Since you're a bit quiet here. I'm going to give you a lead right the way The free energy the relative free energy between these three different phases solid liquid versus gas for water That determines when you move between the phases, right? Imagine what would happen if you had a new phase with these temperatures What would that mean? for all water So take your minute now So the curve just says what is the free energy as a function of temperature for water and you have a solid phase That is the best at very low temperatures. You have a gas phase. That's the best at very high temperatures And then you have this liquid normal water phase that is best at intermediate temperatures The free energy of water So this would be for water and this would be a roughly zero degree centigrade and that would be 100 degrees centigrade, right? Yes For now, I would say let's not even care why But let's focus on what is wrong with this. It's a completely regardless of the conditions. It's completely wrong. It can't be right Sorry, it actually can at the triple point but not that room temperature But I think you're getting close to the answer here. Let's try to draw I I so need more colors here black. Let's see if that one works Let's try to draw Let's assume that poly water was a fourth phase of water here Try to use those two points And try to draw that in diet that diagram And we already know that this is 273 And this is 373 Kelvin, right? So we have one temperature at whatever 523 And let's say that's another one. It's 243 So there's something there and there's something there So the poly water line would have the blue one is ice, right? So here you would have the poly water line being better than ice Because otherwise it would that's why it is melting And here you would have the poly water line be better than the the red Gas one, right? So that the poly water line would have to go somewhere there, right? So what would that happen if you compare poly water with normal liquid water? All water in the world would have to be poly water Which it obviously is not So poly water is definitely not a phase that can be stable Do you see the power of these equations? We don't have to add that. I could not care less what is wrong with that. It doesn't matter. It can't be right And it's kind of scary that it took Richard Feynman That's some other people to realize that it doesn't matter Because the problem is that if you start arguing about their experiments, you're going to be stuck in the details, right? The power of these equations are what here dependent on the detail or the pressure in the tube? Nothing And because it's universal it also means that the result is universal And by the time we've said that sorry, it's theoretically impossible. This cannot be a correct result And again it discovered in 62 seven years later. We're not these are fairly famous scientists They were not stupid But people kept publishing on this for seven years And I think we should have more people sit down with a piece of pen and paper. So this is obviously ridiculous. It can't be true Yep I didn't I didn't I don't know anything about the slope of the line The only thing I know that at this temperature the water is the freezing point, right? So that if I'm below that temperature is better to be normalized and it's above that temperature It's better to be poly water And that must mean that the poly water line must have lower free energy when I go from below 243 To above 243 or whatever the point is That is the definition of a phase transition Same thing when I'm boiling Normally it's better to be poly water, but around that temperature suddenly it must be better to be in gas phase So then the red line must cross And then after that then I just draw a line. I have no idea about the exact line. So Well, I guess in theory you could say that the line should go Something like This I I think the likelihood that that happens is fairly low Because in theory that could happen, of course, but phase transitions are usually smooth So what do you think happened? So there are there are a bit There are actually some papers and I have links about this in the course of survey It's well worth reading this because it tells you something about when science goes wrong So it likely turned out that when you when you have a capillary and if the capillaries are thin enough The amount of water here is exceptionally low While the surface area is relative to the volume quite high So at some point you likely start extracting impurities that might be just on the surface of the glass or something You might even extract some impurities from the glass So there were some arguments that when when people it was it was virtually impossible for them to determine poly water spectra Without having a bunch of characteristic peaks of impurities things relate to sweat For instance and everything that might be in the air and this I think was one of the lead that eventually Put people on the right track that if it's impossible to determine poly water spectra without the impurities The poly water is likely more based on the impurities than water itself And eventually this died out that there was a famous talk by Langmier who's a famous physical chemist who used this as an example of pathological science And pathological science. I think it's an interesting concept. It's literally the same. Well, it's the same word as we use for disease, right? This is not necessary. It's borderline scientific misconduct, but it's not really scientific misconduct Well, we can easily fool ourselves the scientists, and I think that's what happened here, too These were not bad scientists. They didn't want to trick the world But bad results have a tendency to live on forever Which of course brings to the next question. What is science? How is science different from say astrology or creationism? Now creationism is certainly a theory Exactly You can if you can prove if you can't prove a result wrong. It's not science And I think there are certainly people saying this I say at least that's a good definition for natural science There are some cases of social science or humanities and everything where you could argue that you need a broader definition But in real science, I think that is a good definition that you must be able to prove it wrong And there's there's a classic quote by Wolfgang Pauli said it's talking about some student that this is not right This is not even wrong and the point is if it's not even if you can't prove you wrong It's perfectly okay to be wrong But if your theory is so fussy that I can't even prove you wrong. It's not science So that's of course the good theoretical definition, but polly water was definitely wrong and it took people seven years Yes That's a good point Probably probably early sometimes around the natural revolution. I would say we've certainly developed the statistics so But you're also the answer you gave is also beautiful and simple right so that the what if I do an experiment and suddenly I do my experiment on protein folding and suddenly I get one outlier result That means I should give up all my theories on protein folding Because I proved myself wrong So that's not how science works either, right Or you realize with to say evolution that there are of course minor things that we hadn't account for and everything That doesn't mean that we give up on the theory of evolution So science somehow tends to develop more into research programs. Uh, it's uh So that of course if you prove me wrong or if I re-slide this experiment I don't necessarily give up everything we thought about what we tried to modify the theory see Can I imply can I incorporate this strange result in my theory and improve the theory to make it better? So for instance, you could argue that general relativity proved Newton wrong It doesn't mean that we've given up everything we knew about gravity But if we modified the equations and created a better description of this But the protein scores, that's also how bad science works, right? That when you get a result that contradicts you you try to modify your theory try to get more data And I think this is the hard part is that eventually Eventually these results tend to die out, but it frequently takes way longer than we would like to be the case And I think there's another example that bad I forgot to say that that bad theories and everything die out not because people accept that they're wrong But because the proponents of that theory eventually die and the next generation of scientists take over And it's not as or it's not as incorrect as you might think So I'll give you one more example Uh Science is more related to literature than you might think. How many if you have read Kurt Vonnegut? Cat's cradle. Have you read it? So what's cast cradle about? Ice nine Yes, it's a scary ice. So it's an ice. Oh, I should remember this But it's basically an ice form that everything that the ice nine touches And uh, it's it's freezes as like 45 degrees centigrade or something and if the ice nine touches it, uh That spreads to i becomes ice nine two And I think he even got the idea from Enrico Fermi or something This is one of his scientists colleagues who actually gave him the idea. It's pretty scary Could this form of ice exist? Why? Exactly for exactly the same reason as the last plot if that was the case Of course, you couldn't theory imagine an exceptionally high activation barrier But in practice if there was ever one such eye crystal that had formed anywhere in the world Within days at least all the water in the world would immediately move over to ice nine The cool thing is that since then there is actually a real ice nine crystal that we have discovered to There are tons of different forms of ice ice four is the normal one But the real ice nine only occurs at very fairly high pressures and low temperatures 150 Kelvin or so But it's another example. You can explain this with the very simple free-end equations Good, um That gives us the main topics of today Remember what I said that the f equals e minus ts equation was not quite as simple as it might look like It's an amazingly powerful equation. And that's why you need to understand it And just as we can use it to explain some literature and science mistakes We can use it to explain and understand a whole lot of things about proteins So that's my plan today. I'm gonna let's see it's 10 12 I'm gonna spend another get started here with five slides or something And then we're gonna get you a well-deserved break So now I'm gonna head back to the polypeptide chain and the secondary structure But I'm gonna try to formulate things with less hand waving and more free energy than we did the very first lecture So already now I don't think I showed you this plot. We talked about the energy landscapes, right? And here too energy landscapes is a very good model to think about because it helps us understand Roughly what happened and in this case I'm even going to draw a single one-dimensional landscape And this is this is hand waving But you can think of the landscape as somewhere if we start out here And on the y-axis we still have energy and we want to get the lower energy But somewhere along the road here, we could also think of things in terms of entropy So when we start out our chain or protein or whatever this is quite stretched out We don't have a whole lot of favorable interactions yet But we have a lot of freedom the chain is very mobile And as you're moving down this energy landscape to lower and lower energies and we become collapsed As we are collapsing the chain the first step of that would be the multi globular we spoke about last week, right? What happens to the entropy as we collapse it? We become more and more restricted. There is less and less space available to move And that is bad And that's the complication here right because again f equals e minus ts a low e is really good But as we're going down in energy With these chains, we're also going to go down in entropy So there are one out two things that can happen there We either we go down in energy quicker than we go down in entropy and then we will somehow be able to find these states Or the energy drops too quickly And then we're somehow going to be stuck on the way because we can't really move anymore And the energy barriers are going to be too high So whether protein folding happens or not is going to be based on a balance between energy and entropy We need to gain energy faster than we lose the entropy Because otherwise we get stuck And the way if we do that in a slightly more realistic fashion with at least a two-dimensional landscape You frequently see this sombrero like structure So in this case we want to get to the center whether it's purple or something deep down there And then we start out here at the green one So what's going to happen the native protein is down there in the center while the unfolded one is we start out here And you see the red or the black lines here There's some are going to need to cross the first barrier and then they're going to end up in some sort of intermediate state here That's what we call the eye state And then depending on what the energies are we will jump across the second barrier there and hopefully find the native state But this is then going to depend on how good is that state versus how high is the barrier to the real folded state And this is just in two dimensions. You can imagine how many traps there would be in 100,000 dimensions And it turns out that we can frequently measure this in experiments So you can measure these rate constants and you can identify that there is some unfolded state And there is some sort of native state and we might be able to identify some intermediate states For instance by the amount of secondary structure we have in it I will show you later today how we can determine that secondary structure And if we measure this of time we might also be able to see how fast do we move between the unfolded and the intermediate state And between the intermediate states and the native states and based Well, for instance based on those rates and the detailed balance we can actually determine the free energy of these states too And friend of order would then say, yeah, that's all good and well in theory But that does work in practice and it actually turns out that it does work in practice So this is an example of a curve. I think it's determined from NMR when we have some very simple reaction coordinates And we can show that depending on the temperature and everything the protein will actually spend time in all these different states The blue one there is going to be the best But we also spend time in these regions in these regions You probably can't see it really beautifully there But this is a completely unfolded protein. That is the completely folded state and that is Some sort of intermediate states And the way we define these Of course, these proteins would also need 100,000 degree L at least 10,000 degrees of freedom So the way we define this is that we might have some sort of spectroscopic probes So we can measure what is that particular hydrogen bond formed or what is the distance between these two residues with NMR So we find some examples of reaction coordinates that describe how compact the protein is But the take-home message here is that this is not just based on very simple theories This actually works in practice too So let's start go through these secondary structures But now we're going to think in terms of delta g and identify the entropy and enthalpy for all of them And we're also going to think about what happens during folding So before we look at the secondary structure, what is this extended state that we see here at the bottom? So that's an all-trans chain of polyalanine in this case We remember what I said about that on Friday. Is that a good representative of an unfolded state? Why? Yes, or you could say that it's It's just as good or bad as all the other ones, but there are hundreds of billions of them And the point is that it's not that all unfolded proteins are stretched out in general Unfolded proteins are going to correspond to this molten globular we talked about on Friday Because we don't want to turn the hydrophobic parts to the water So all so we think if we start with this state And think of terms of energy and entropy Is the entropy high or low for that state? If you just look at that particular confirmation, why why is it low? Right It's well ordered, right But do you think of the unfolded state as a collection of all the states that are not say helix or sheet? If you think about not just a specific confirmation For that type of unfolded collection of state is the entropy high or low High because there are lots of states like that, right? So the reason why you want to be unfolded is because the entropy is good high entropy to be unfolded I'll come back There is another caveat there that actually in that incident we also explains why proteins have to be chains But that we will talk about after Easter Energy on the other hand that's going to depend on the amino acids in the unfolded states In this particular case it would be horrible because we would turn all the hydrophobic parts to the water Which would force the water which would break hydrogen bonds And then we would require the water to form a clathrate around it which would be an entropic effect On the other hand if these were polar amino acids the energy would be quite good So let's move to the secondary structure since that alpha helix first So what happens with the energy and entropy when we form an alpha helix? Why? Exactly So now we need to think macroscopic again, right on the one at all the unfolded states That's one macroscopic way of thinking for protein tons of them alpha helix It's pretty much only one you can't move a single torsion more than a few degrees that we would break the helix So it's an astronomical drop of entropy to fold an alpha helix The reason why we still form an alpha helix is that we end up with all these beautiful the yellow dots here the hydrogen bonds So it's a well packed structure and there are tons of hydrogen bonds formed in it Which is particularly important on the inside of a protein because on the inside of a protein We would otherwise need to turn these oxygens and high and polar hydrogens to other hydrophobic residues And for a normal alpha helix We also always have this pattern of i to i plus form forming hydrogen bonds Which means that every single both the hydrogen and the oxygen in every single peptide bonds apart from a few at the very start And a few at the very end would be involved in forming hydrogen bonds Alpha helix is a it actually turns out that alpha helix is in titratable amino acids they frequently occur together And the reason for that is An alpha helix is very simple, but it's also not as simple as you might think So one property of the alpha helix is that it's periodic, right? So you turn 3.6 residues per turn So 3.6 residues later you're going to be back on the same side of the helix where we started So this is a small sensor that is part of a membrane protein I will cover this more when we talk about membrane proteins But inside this membrane protein you have this particular helix is actually going to move up and down When we change the voltage across the membrane and then there are a bunch of charged amino acids here actually arginines And you see how they sit on the same side And because they sit on the same side they can kind of form a stare Uh, well, so sort of step ladder things that they can gradually move from one point to another And swap hydrogen bond partners with each other. Yes So titratable amino acids were the charged ones the ones that the ones who serve I usually call them titratable because they're they're arginine lysine glutamic acid aspartic acid and some and histidine And another way would be to call them charged But they as I say in the inside of the protein they might not be charged And rather to have to constantly explain that they might not be charged calling them titratable amino acids is an easier way Let's see if I even have a movie of that. I don't remember. Yes So do you see in this particular case that the entire structure is moving? I'll come back to later on why it moves, but this turns out you see that Do you see that there is it made a jump and that That aspartic acid here that previously was interacting with that one is now interacting with that one This happens inside your cells every time you conduct a nerve signal in your nerves And it happens in like 200 microseconds or something And in your heart to all the time. This is the basic of bolted skated ion channels And the reason why I'm showing this already now is let's see that the entire alpha helix here actually stays intact all the time We don't unfold the alpha helix. So we can have this protein undergo through a fairly large Confirmational change here, but you have the entire secondary structure element moving You don't break the secondary structure. You don't refold the protein but By having some conformational changes up in the loop I can take this entire helix and move it either up or down And it moves like one or two nanometers Which does not sound like a lot, but it's probably the most fascinating miniature machine in the world It might yeah, you mean that part up here. It probably does a little bit This is a membrane protein. This is the ones we care most about are the ones in the membranes So why do you think the alpha helix doesn't unfold? We're forcing it to go under through fairly major conformational transitions, right? Wouldn't it be reasonable to think that it could unfold? Exactly, right? It's stabilized by all these hydrogen bonds and we would pay an insane amount of free energy by starting to break the hydrogen bonds There are a couple of different ways you can draw the alpha helix. I kind of like this because it's a good way of understanding that You need to know that the pattern in a normal alpha helix is this Residue i is hydrogen bonding to residue i plus 4. It's a very characteristic pattern of an alpha helix And what happens with these other helixes is again 413 is alpha If you squeeze the helix harder, you're going to move so that residue i is bonding to residue i plus 3 and then it's a 310 helix And if you squeeze it looser you would have i to i plus 5 which would this with this pi helix Forget about the 217 helix And what i didn't show you at the previous slide, but it's pretty cool. I will show you that again What actually happens when this undergoes the transition is that right here in the middle There is actually a small part here when the helix moves over to a 310 helix right in the middle Can you imagine why it would you probably don't see it that well here? Why would it like to move over to a 310 helix? It is not an e well Not an entirely trivial model Remember what I said about the alpha helix? How many residues per turn are there there? 3.6 In a 310 helix, how many residues per turn are there? So if you you can actually draw something called a helical wheel So if you draw the helix here, we draw residue say zero there And residue one there And residue say two there Residue three there. This is not that good and then it would be residue four there And residue whatever five there. So you see that would be offset that would lead to the spiral stairway On the other hand, if we have the 310 helix With a 310 helix, there are exactly three residues per turn So we would start with zero one two three four five six seven No, sorry, I screwed up there I drew that as four, but you see the point right? So that if you have a protein like the one on the previous slide In a 310 helix, these chart side chains would be exactly superimposed on each other So if you have an alpha helix If you're going to move this up and you're going to need to have one chart hydrogen One chart side chain take the place of another one You would also need to rotate the entire helix and that's problematic because all these side chains are interacting with other stuff But if it's the 310 helix, they are exactly on top of each other and then you can just move the helix vertically So normally a 310 helix is not as good as an alpha helix But there are a few places where it's directly very convenient to have But we'll come back to talk about membrane proteins but that's The point there is just that under some Under some conditions it can actually be more favorable to have in particular 310 516 is very rare and 270 and I've never seen So you probably already saw this but that's again just to stress the part that I said that while the hydrogen bonds are important It's important. Remember that this is not what an alpha helix looks like This is our beautiful way of representing it. It makes sense to us But the way it actually this is still a collection of atoms and to really understand this you're going to need to look at every single Hydrogen bond and the rest of the chain here So is it only the hydrogen bonds that matter for the alpha helix? So if it was only the hydrogen bonds that mattered all residues would always form alpha helices, right? Which they obviously don't do So what else is required to form a stable helix? Sorry Sorry Yes, but what is required of the rest used to form a stable alpha helix? Well, they need to form peptide bonds, but again all amino acids form peptide bonds Sorry, you said there was something here. I didn't listen. I didn't hear at least Periodicity, but well So if I just take proteins that's a periodic sequence So they they should not clash right and they should all All these torsion angles throughout the selix they need to be in regions where there is no stereo clashes And where the protein is fairly happy to be with the angles that correspond to how alpha helices And that's not universally true So if we look at that's what we have these ramachanan diagrams Is that some regions the right-handed alpha helix here in particular are better for some residues than others And if you have a particular rescue that is not happy here, it's not going to like to form an alpha helix And that is the case for instance for proline Proline does not like to be here. Why doesn't proline like to be there? It's bulky, right? Then it has this built-in ring. We'll come back to that after the break. I think But then another question for you. This doesn't make sense. If you look at glycine is glycine bulky Glycine can be glycine's ramachanan diagram is more Spacious than any other ramachanan diagram. We know right glycine can be almost There is no other residue that can be in so many places in this ramachanan diagram as glycine But glycine doesn't like to be in alpha helices Why? Well flexible is good, right? Flexible means that it can definitely be there Yeah, but I can form that with the hydrogen bonds Well small is good if you want to fit something if you want to fit something in a hole the smaller the better Now we're getting closer It loses entropy, right? Because glycine is so small when it's not in an alpha helix it can have much higher entropy than other residues And now we're suddenly going to take this very flexible residue And force it to be stuck in a very small part of the ramachanan diagram, which is suddenly just as small as the other ones So for glycine the drop in entropy when it moves to an alpha helix is more severe than for the other residues And that's why glycine doesn't like to be an alpha helix So this is kind of cool the reason why proline and neither proline nor glycine like to be in an alpha helix But they're completely opposite reasons why they don't want to be in an alpha helix But probably it's because of the steric clashes for glycine is because we would force it to lose too much entropy Um, it's actually 10 30 now. So rather than me storming on to beta sheets I would suggest that let's take our 30 minutes and Reconvene here at 11 sharp And then we'll talk both about beta sheets and then turn and a couple of other things Because glycines are important for some things in life. All right Beta sheets beta sheets beta sheets They are completely different from alpha helices, which I hope that you agree with Rather than me going There are a couple of things we already touched upon here One thing has to do with how we form the interaction global versus local, right? So in this case they enter there are still tons of hydrogen bonds and just as alpha helices Most or virtually all peptide bonds here are going to be paired not they're going to be some Ones at the end of each sheet that are not formed The other thing that I might have mentioned but that becomes a little bit more important now The beta sheet nomenclature is well known out of where the beta sheet nomenclature is well known And the beta sheet would be the entire collection of all these polypeptide Backbones here that form a large extended sheet What is not quite as common you might is the beta strand and when I say beta strand I typically mean one of these chains just the second chain here that forms a beta strand So one obvious thing is that if you look at one beta strand, it's the same issues with the alpha helix, right an individual beta strand corresponds to that completely straight style Well pretty much unfolded amino acid and that is an exceptionally unlikely confirmation from an entropy point of view There is only one way to put it there is that's just stretched out. It's the chain in all trans So individually that is a horrible confirmation The reason why that exists is of course is that when you have multiple ones formed like that They can suddenly form hydrogen bonds between themselves and that pairs up all the hydrogen bonds in the structure First is for where are all the side chains pointing? Actually exactly so either towards you or into the plane here So they're going to be you have one plane formed by the entire sheet and the side chains point out of that plane in both directions So we think about the beta sheet here. What are the important? What are some important differences going to be when you form a beta sheet? So we didn't I didn't explicitly cover that for alpha helices, but for the alpha helices How does an alpha helix form and I'm going to go through this in much more detail in a few days. Yes Right, but I'm not so much thinking I'm thinking like how it forms right that we need to place these amino acids and this We need to form the torsions so that we start forming the spirals there And when we put the first residue there, it's bad because we only lose entropy when we put the second there It's still bad when we put the third there It's still bad and when we put the fourth there It's still bad and then we put the fifth there that it's i to i plus four then we start gaining our first hydrogen bonds So you can already now we can say there's going to be a bit of an uphill battle initially when we form an alpha helix And by the time you come to four five or something like that Then we're going to start gaining entropy energy because we form hydrogen bonds If we look at beta sheets, what's going to happen here? So the point is yeah The point is that we need to put this entire backbone in this confirmation, right? Then when we start by putting a backbone in this confirmation, there is still no gain And then we need to put an entire second backbone in that confirmation too, which is also very unlikely But when we do that, we don't just gain one hydrogen bonds But then we gain what's the one two three four five six seven hydrogen bonds So already here and we're going to see this later You can kind of study that it's going to be probably more of a barrier here because there are more residues We need to put this way But once we get to the top of this barrier, it's going to be a very strong Form that will likely take longer for beta sheets to form. Well, that's still a bit of hand waving I also mentioned that there are two ways of putting this And here's where it helps if you can draw your amino acid backbone So you have n c alpha c n c alpha c n c alpha c n c alpha c and then the hydrogens and the oxygens Pointing out. So this chain is going in that direction And here we have a chain in the same direction n c alpha c n c alpha c So this chain also goes in that direction And to pair off or pair up all the hydrogen bonds here You see that these hydrogen bonds are going to be a bit well not tilted But they're not going to be completely straight. So they have to point in slightly different directions Which is reasonably okay But it's not quite as good as if I take this chain that goes left to right And then I pair it with another chain that goes right to left So here we have n c alpha c in that direction And when they go in different directions, you see that all of them are going to be Perfectly paired up with each other. So this will be just so slightly better But both of them are good and both will happen There is another reason I would argue why the top one is slightly more likely So that we have names for this the first one the lower one would be called two parallel sheets The top one would be called anti-parallel sheets Yes Exactly so that when I'm at the end of the right here, right? I need to find something else for me to go out of the whiteboard or something and form a completely different Helix or whatever some other structure so that I can come back there And that would definitely take a bunch of residues It will depend whether that is a loop or alpha helix or something And that means that it's going to be a longer drop in the helix between these two sheets While when they are anti-parallel I can go in one direction And then you're going to see that I can turn around pretty quickly and then I can go straight back So the anti-parallel ones is like drawing a pen you can just go up down up down up down up down which is a bit better The other thing that happens with beta sheets is that because of this because of the way the backbone looks They're actually going to be a bit zigzagged or pleated So that this is harder you can't see this in the simple schematics But if you look at the residues it's going to be a bit of that effect But here we see more clearly the yellow dots here are the side chains So what do you see with the side chains here? So remember the pattern I told you about the helix that there is a pattern of say 3 to 3.6 Here there is a pattern which is every second Can you imagine using these patterns anyway? Nature will use them So in particular let's start with a beta sheet that might be here So if you take a long stretch of beta sheets And then we make every second rest you hydrophobic and every second rest you hydrophilic Then you're going to have one very hydrophobic side the upper side here would be hydrophobic while the lower side would be hydrophilic Which is kind of a neat way to separate things you would have you would effectively have a surface where one side of the surface Is hydrophobic and the other side is hydrophilic I'll show you how to use that shortly And I also mentioned that these sheets will be just a bit twisted that On the one hand, this is a small The reason for this is that you're going to see it all the time in structures and I want to explain why it happens So when you just look at the simple model and even the previous slide this looks so plain simple completely beautiful sheets Anytime you see this in proteins, they're going to look on the right You see that it's the entire sheet is turning a bit, right? And that is not something special based on the protein or something but what happens is that Inside each of these strands The torsions here they're going to be almost they're going to be placed so that it's almost exactly trans But they're not exactly 180 degrees, but there might be 178 degrees or something And for one or two amino acids is not going to matter. They will look completely straight start But when you end up repeating there's lots of times, right? You're going to slowly slowly slowly going to turn from that completely straight part So what's going to happen is that if you go if you start here You see that you're always turning slightly clockwise if you move in the direction of the sheets So you're slowly slowly slowly turning And when you then combine this into a larger sheet That's it's going to mean that the entire sheet will actually have a bit of this turning property too So exactly the direction here is not important and everything But that's why you look inside any protein structure. The sheets are never going to be completely planar or at least that's very very rare So with that we know a bit of the unfolded state We know a bit of the alpha helices and we know a little bit more of the sheets But there is one thing I've ignored We also need to move between these secondary structure elements And I think all of you take most of you at least have taken the bioinformatics course And occasionally when we try to predict secondary structure, you might try to do a three state prediction You try to predict helices beta sheets and coil and coil would be everything else that's unordered But that's not exactly how it works In many cases, in particular, you have these large anti-parallel sheets If you have these very short turns actually, sorry, this is a parallel sheet. That's better Here if you have a very small turn here from the end of one strand to the next one That's not really going to be a long loop. You want to make these as short as possible And nature does that So these turns they're so short that they're almost they're not just almost they are effectively part of the beta sheets So if you are here, if you're having one chain going here It turns out you can put one residue here and then one residue there And if you put them in specific ramachandran torsions It means that within two residues in the turn you can end up with the chain going the other side And this is just slightly different ramachandran torsions of the turn But the point is you can have this very very very efficient super well packed things with just two residues And then there turns out to be a number of different turns you can do but type one and two by two are by far the most important ones So you just need two residues Can you imagine what residue is really convenient to have in turns? When it's this tight and very well packed Yes, why? And here you need the stereo there is simply not a whole lot of room, right? You don't want to push in large side chains or anything here But it's of course it will still be an entropic drop for it So but it's happier in turns than any other residue and we need these turns to be able to fit To have any sort of continuous sheets The reason for just for having this slide is that these turns are these turns are so well known So occasionally when you predict secondary structure, you actually call it a four state predictions You predict helices sheets turns and coils So you separate the turns from the coils because it's fairly we can recognize this when there are two When there are lots of beta sheets and then there are certainly two glycine residues And then more residues that are likely beta sheets Then we know that it's not it's a turn in the beta sheet and then you go back The reason why secondary structure is important is that we turn we can determine it we can determine it with fairly simple measures One way of determining would of course be to determine the full structure of the protein but x-ray crystallography or cryo-eum Why don't we do that? Too expensive and too slow And the poor point of understanding if you already have the entire 3d structure of a protein, there is no point We want secondary structure for two reasons either because we really really would like to see quickly what this protein is Or we might want to see that what happens if I change the temperature here This is actually some very nice techniques to see what happens during folding But if I want to examine what happens during folding then by definition, I'm going to be changing things, right? Then I can't My one of these cases might be at room temperature and another one might be at 60 degrees centigrade I can't determine the cryo-eum or x-ray crystal at 60 degrees centigrade because then I don't have crystals So by far the simplest method to do this is cd spectroscopy Which stands for circular dichroism Remember lecture one that all amino acids are chiral And the chiral property of amino acids will turn out that if you send circular polarized light on them They're going to twist this light slightly different in the left versus right hand direction Depending on the amino acid and in particular the amino acid surrounding and this surrounding is determined by the secondary structure So you measure this in a fairly complicated mind called ellipticity And I'm not It's not important exactly how you measure it But the point is that depending on whether a structure is alpha helix beta sheet or random coil As a function of the light wavelength You can end up with different patterns in these cd spectra Do you have any idea how long this takes or how costly it is? it's like One minute And we probably there are probably 20 cd spectrometers in this department If you don't have any cd spectrometers, we might have to buy one and it's A low end one is probably a few 10 000 kronor or something. They're very cheap instruments And they're very efficient because then I can take the same sample heat it to 50 degrees centigrade And put it back in the cd spectrometer And I'll see whether anything changed And if my helix now unfolded it will have moved from the red curve to the Blue to the the cyan there So it's super super super fast simple The drawback is that I have no idea what's ever about sequence The only thing I will know roughly what is the fraction of alpha helix versus random coil versus beta sheet in the sample So it's a poor mass technique but very efficient Slightly more heavy handed is to do nmr spectroscopy with chemical shifts And the main advantage of nmr then we can Get the sequence resolution so I can actually get a fairly accurate result What is the secondary structure in the sequence as a function of the amino acid sequence? So why don't we do that all the time? Yes, so we have a cd we have a multiple nmr spectrometers in this department But it's suddenly an experiment that takes a day. It's complicated to do. You probably need to spend the week analyzing the data And you need more protein for it than everything. It's not worth it So which one would you use in practice? Any other suggestions? exactly 20 years ago, I would do people would you see this spectroscopy today You just do it with bioinformatics. So how accurate are secondary structure predictions today? Yeah, 85 to 90 percent But so why But again, shouldn't we use experiments so that it's 100 percent accurate? Exactly the point is the reason why we can't really it's hard to get to more than 90 percent No matter what method you use because at some point you get to the end of the helix Where is the end of the helix and the beginning of the coil? Again plus minus one residue there can easily make five percent if they well if the helix is 20 residues long one residue is five percent That's going to depend on temperature. It's going to depend on the surrounding. It's simply not that well defined So for all intents and purposes 90 percent is as good as you need to be So today we don't Unless there is an exceptional case where it's really important that the prediction methods are bad Today just go into the computer and let bioinformatics predict. It's good enough So if we compare helices again helices are formed entirely by local hydrogen bonds while heli sheets are non-local hydrogen bonds The helix can grow. I didn't say that explicit It's we I hinted that it can grow fairly fast But the point is it can grow gradually you can add one residue at the time to an alpha helix once you have the first two terms And the initiation barrier you just need four five residues to have formed the first turn in an alpha helix And you can gradually start adding to it Beta sheets on the other hand either you have a sheet or you don't you can't add it's very hard to add one more residue to a sheet And this also means that there's a very high barrier because you need to take two entire strands and put them in completely stretched out manner Which is very bad entropy wise And it's not until they actually have formed all those hydrogen bonds that you're going to start to gain anything So already here we can predict that it's going to be a fairly high initiation barrier and beta sheets are going to be quite slow to form And later on in the course we will actually show that this is even a phase transition in most cases There are also different amino acids that prefer to be in helices and sheets Helices in particular hate proline because proline is going to be very If you put proline in here proline is going to break at least one of the hydrogen bonds that keeps the helix together And you can see that how do you see that? the structure It will kink the helix Because just to fit that round it's going to be a 10 15 degree kink in the helix And this is so strong so you can even see this evolutionary when there are families Where some members have had a proline all of them will have that kink even the ones that don't have the proline yes um It depends no, I wouldn't say pi well It has to do with the definition So when is thing a helix right when I think it's a helix So the pi helix in particular had to do with this pattern Whether you have 5 16 pattern in the hydrogen bonds and in the particular case You're right in the sense that it's going to be unwound a little bit But since you don't really have that hydrogen bond, I would not call it. I personally would not call it 5 16 helix And the rest of the helix both before and after that is the standard 3 4 13 hydrogen bonding pattern, but you're right that it's a bit unwound Beta sheets on the other hand have a much better tolerance for glycins because they like Glycins in the turn from the end of one sheets the next one And they also have a bit more room to fit a proline inside the beta sheet Although proline itself is fairly happy to be a loop stoop And apart from that You've gone through the bioathematics that are other sequence patterns So that many of the small and had a phobic residues actually prefer beta sheets to Let's see. We already talked about proline being rare in helices. We talked about glycine being common in turns Some residues are very common at helix ends. I think I have a slide about that later on And we also have yes Well, they are but For proline and a particular glycine for some of these residues the pattern is so strong that one residue can pretty much destroy a helix Or it will be in the end of the helix For other residues, there are certainly residues that prefer helix or sheets But nature also has some sort of built-in stability To random mutations. We will talk about that much more later on in the course that so one single mutation In an alpha helix with a residue that kind of prefers to be beta sheet is usually not enough to disrupt it It's not good, but it's not completely going to kill the helix So most virtually all residues have a preference for either helix or sheets or turns It's a combination of steric hindrance and how much Sorry, steric repulsion in the rimechana diagram so much. It likes to be there And it part also how good it is at interacting with other residues in the surrounding in either in the 3.6 repeat or the the twofold repeat So how do you think we know this? Yes, or simple just statistics, right? Homology would have mean that they would have to be related But you can also just count look at all out. That's how that's actually one of the starts of bioinformatics So called the two fast man rules That two and fast man started look at all the helices and beta sheets and all the structures that had ever been determined And for every residue we like how likely is it for this residue to be in helix versus how likely is it for this residue to be a sheet And from that you could infer by the bolstering version, right? That there's some sort of delta g does this residue like to be in helix or sheets And then you essentially do a running average over roughly four residues And based on that they could predict secondary structure with amazing accuracy. I think it was 35 percent So that's the reason I think the book even goes through two fast man So you can laugh at this But in the 70s this was pretty darn sexy And what even when I even when I started these courses in the early 90s two fast man You we went through and did exercise some two fast man The reason for message, can you imagine the advances that bioinformatics have gone through? We moved from 35 to 85 percent in two decades Yep No, so well, so the two fast man is probably oh no, no most things are helix or sheets It might have been so I might have been too low. It might be 45 percent The point is that For proteins in general there are quite both a lot of coil and helix or sheets It's probably a third of a bit for a third of each Two fast man might be 50 percent or something. I don't remember But the point it's clearly better than random But it's very far away from what you can do with bioinformatics today So what we're going to go have a look at some of these differences and see whether they can be useful So the first thing that we can look with all the amino acids is look at their relative abundance So here you see the abundance here is exactly the fraction Let's see. This is exactly the fraction that they occur in proteins. What was that determined from again? We talked about that Coat on frequency in the genetic code. This has nothing to do with proteins or homology or anything When you predict them you might rely on homology and everything but the abundance itself is just based on nature We can also calculate the delta g for salvation in some cases It's so when this is extremely high. It's even hard to determine this accurately But these numbers are so high again compare this with kt So this is k cal the kt is 0.6, right? So this is 100 kt So the likelihood There's e to the power of 100 the likelihood that they're not the likelihood that they would like to be Prefer to be an oil instead of water is zero. It doesn't happen But then there are also going to be patterns with some of these whether they prefer helices or not So let's start with the obvious ones proline first the problem with proline is that Well, it's not a problem. It's a proline has this ring after the c alpha you move out And then is the the last carbon here binds back to the nitrogen So a normal nitrogen would have a hydrogen here, but in proline We have this ring formed and that is exactly the hydrogen that would need to participate in the hydrogen bonds in the peptide group So the proline is missing that Technically proline is not an amino acid if you really this is not something that's going to decide it But it's so called an amino acid and the department of use this knowledge This means that proline is it's proline is not really happy either in helices or sheets It's somewhat happier in sheets than helices, but it's turns or coils or something It is hard to pack this efficiently with anything Glycine in particular is exceptionally small and flexible which on the one hand means that it can fit almost everywhere in particular interns The caveat there to remember for glycine is also that means the second you actually do put it anywhere We do an astronomical loss of entropy which is bad in particular for helices And then alanine is the first real chiral amino acid alanine is you could argue that alanine is boring But boring is good if you're a amino acid alanine can fit pretty much everywhere either helices or sheets It's a bit hydrophobic and it's a bit hydrophilic Pretty much almost plus minus zero. You can easily have alanine on the surface of a protein You can easily have it on the inside of a protein for nature This is an awesome building block that you can fit pretty much everywhere And then you start to be larger and hydrophobic Remember the point that I said that you don't necessarily need to know all these amino acids by heart So what is the difference between valine isoleucine lucine? They're larger than alanine and hydrophobic If you want to in terms of understanding the structure, that's enough. Yes At some point you wouldn't need to look out and maybe draw them or something But in your gut feeling You only need to know that oh now you start to have something that's big and bulky So they're not you're gonna have a side chain that absolutely doesn't it's definitely hydrophobic It's bulky. So you somehow need to put it on the inside of a protein. You will not be able to fit it in turns Can you have it in the helix? Sure, if the helix if this side of the helix is facing the inside of a protein You can always have it in a sheet too if it's on the inside of a protein And the way we enumerate all these carbons is that the first one would be the alpha You know what the alpha carbon is and then you just continue in the grief alphabet beta gamma delta, etc So we just say beta carbon. That's just the first actual side chain carbon But they're pretty boring in this as they're just hydrophobic. They don't do anything those carbons So that's why we don't really that's why we group them Cysteine is A somewhat hydrophobic molecule, but cysteine is important So cysteine contains the sulfur group or thiol group The important thing with cysteine is that under the right conditions You can lose that hydrogen and form a bond between two sulfurs if you have another partner assisting group And that's actually that's not just it's not like an hydrogen bond or anything That's a very tight covalent bond and when you form it it will not break And you use that all the time in the experimental lab and you do the cysteine scanning and everything because if you place Cysteine's in the right place you can check whether these bonds are formed and if these bonds were formed That where even if you don't know what the structure was right Where I placed my two residues they must have been closed to space Otherwise this bond would not have been able to form And then you can get a structure like that This looks completely boring What do you think this is? Random coil That would be my bet Let's give it a bit more detail Still completely unintelligible. It's just a random piece of amino acids So you see here you have some cysteines here. So here you have two cysteines One cysteine in that green chain and another one in the blue chain Do you see that they formed a cysteine link there? And here you have one in the green chain and one in the orange chain It's another cysteine link there And here you have one in the orange chain and one in the blue chain and they form the third cysteine link there So this is a protein that doesn't really have any secondary structure It might be a tiny amount of beta sheets among them But what all those cysteines do they create a very rigid almost not like structure So that if it was not for those cysteine bonds, this would be a random coil But with the cysteine bonds they form a very well-defined and strong structure And it's even it's even called a cysteine knot This is using spider toxins. There are lots of tarantula spiders and everything Which tends to hit the multigated channels in your nervous system It's a it's a very classical example of a fault and again, this would not be a fault without those cysteines Some of the ligand gated ions are even called sys loop receptors because there is a specific cysteine Dysulfide bridge in the structures So these structures are usually very important And they form so if you again they form this might seem obvious here So we have one side one chain here on the left with the cysteine and then one chain on the right with the cysteine Then you for each cysteine you have these torsions the first torsion and the second torsion in the side chain And then we can call them prime on the other side the first torsion in the side chain and the second torsion in the side chain What will a cysteine bond or a bridge? Due to the entropy of the system So this will be a fairly dramatic reduction of the entropy right because you have two chains that in principle think of the cysteine not The toxin I showed you two side chains that are in principle completely free and flexible And then you lock them in completely relative to each other so they can't move at all So if there's a gigantic drop in entropy, can you say anything about how much energy we gain or lose from forming this bond? We need to gain a lot of energy from this bond, right? Otherwise it would not happen tryptophan is another friend There's a big and bulky residue But it's not just hydrophobic So you have one part of the tryptophan that has this Polar part and an n-h group there and then another six-member carbon ring So one five-member ring that is a bit polar and then a six-member ring that is a bit bulky And it's an indole group the polar one if you really want to go into the details This is a very difficult to pack residue And you do scannies here in experiments too that if you think you have a binding site or something You can try to mutate an alanine for tryptophan because the tryptophan might fill up the entire binding site And then you might not bind there anymore. So if you want to test by pretty much trying to put something large in a protein We always do to tryptophan And tryptophan is pretty cool So tryptophan is parts of the world's smallest protein which is called the trp or the tryptophan cage by anderson So how do you define a protein? So that this is difficult to finish them with other I would say that things become a real protein when there are some residues There was a well-defined structure and there are some residues that are entirely inaccessible to the solvent And that has to do these things even if you just have a stretched out chain There might be some residues that prefer to be in an alpha helix or something But there has to be something more than just a little bit of secondary structure And by the time there is at least one residue and in this particular case tryptophan That is completely buried and they have other residues around it Then we start getting to these concepts that we talked about the The multi globular or for instance you have some sort of hydrophobic things on the surface Sorry hydrophilic things on the surface and hydrophobic things in the interior And the cool thing with the trp cage is that this protein is so small that people have even been able to simulate how it falls I'm going to show you that in a small movie. So I think this is the tryptophan sidechain and Then you have a bunch of residues before and after it And you can probably see what's polar here. So let's start the movie and see what happens Do you see how quickly it collapsed? Instantly and there's water around it here and now this it's searching here It's well, and it's unfolding again folding unfolding and eventually I think we'll get to a structure where you see the tryptophan buried in the middle and other residues surrounding it And this probably takes on like oh, I think there we are So here you actually see the tryptophan, but that's because we're not using space filling for all these other residues So the tryptophan here is in a hydrophobic interior of the protein And that has looked in the entire protein around it and now it tends to stay folded You can probably almost count them. I think it's in the ballpark of 20 or so. I should know exactly about it I'll text you remember roughly 20 This was just a bit of piece to wet your appetite what happens during folding The other part you see how flexible a protein is This falls in a microsecond real proteins probably takes a thousand times longer or a million times longer We also had a bunch of Polar or charged residues The polar residues frequently occur in loops or turns why But why don't we want tons of loops on the inside of proteins? Well, so now we're in a chicken and egg problem, of course, but One problem with loops is that it's difficult to pair up all the hydrogen bonds in loop, right? So it frequently makes sense how the well ordered secondary structure elements on the inside And then we have loops and turns and everything on the outside on the surface of things when we basically turning around and heading back into the protein A membrane protein is even simpler Then you have the helices in the membrane and then you have the loops when you go out and then you go back into the membrane And for that reason it makes because these they frequently occur on the surface of proteins that it's really convenient to have polar residues there Polar residues can hydrogen bond to water certainly But they can occasionally also hydrogen bond to the backbone of the polypeptide chain Which is important in a turn because a turn will not have the polypeptide chain Form hydrogen bonds with other amino acids, right? So suddenly you can have the side chain of one amino acid form a hydrogen bond to the backbone oxygen or hydrogen of another turn Or sure of another amino acid So let's draw a protein If I have a helix here And then another helix here And then it has a loop between them This loop by definition doesn't form hydrogen bonds With its own backbone because then it would be a helix or something, right? But that means that we're now going to have unpaired Polar things here both in the backbone and on the side chain And they will have to form hydrogen bonds with something else The question is do we have something else here that is good for them to form hydrogen bonds with if this is a perfect helix We just had a phobic residues. That's not going to work So then we need to place a secondary structure element so that we have other polar or charge things Maybe another loop or something here. So it can happen, but it's not quite as common On the other hand if we put them out here a loop here That's going to be very easy because all these all these side chains can now form hydrogen bonds with water So this is not it's by no means impossible, but it's slightly less likely And remember remember this thing that we told we talked about the hydrophobic effect last week, right? The first thing that's going to happen before you even formed all this secondary structure Is that we're going to try to pack all the hydrophobic things on the inside and the hydrophilic things on the outside So they already start out on the outside So I'm not saying that it's impossible and I will not eat my left shoe if we see one because we we do see ones here, but it's If I show you say a threonine and you have to take a guess Where do you place it? If you don't know anything else place it outside But again, this is likely or dead. This is certainly not impossible, but maybe 80 20 Charge residues are like polar ones, but everything is much more extreme charge residues do not occur in the surface Sorry, they do they do not occur in the inside so Let's say that I show you my same beautiful new structure of a protein the lindahl protein And then we place the arginine there So what would you say? That's like that's likely not a very good model. There is something wrong in the model And that has to do I'm not saying that that can never be true, right? But it has the same thing with the free energy reason that Start by using paper and pen and the thing that sits on top of your body think about it the like and Again, there are exceptions these iron channels I showed you because suddenly I'm showing that There is a d there And suddenly I'm much happier because obviously Suddenly it makes a whole lot of sense in this model that I placed them right next to each other So they will form a salt bridge there But if it's just one it's going to be so expensive that it can't happen Of course one time in 100 you would be wrong But 99 times after 100 you would be right based on that gut feeling so trust the gut feeling The exception that's sorry. There's not so much an exception But they still don't occur on the inside of proteins They will occur in the surface But there is one particular thing that happens with helices Remember that We talked about the peptide bonds in the helix and that each peptide bond has a dipole. Do you remember why? So, let's see if I draw n C a c n C a Do you see how I draw amino acid backbones? That's always all trans and then I start with the pattern n cac n cac n cac And when I draw that pattern I start bothering about the rest then there must be a hydrogen there There must be an oxygen there. There must be a hydrogen there. There must be an r group there Must be an r group there and must be an oxygen there Uh, and in particular here, we have a peptide bond, right? So that is the bond that's doubled that we can't turn around So here we have a slight negative charge. We have a positive charge slight negative charge and slight positive charge So there's going to be a fairly strong dipole pointing in that direction above each peptide bond And in an alpha helix what's going to happen is that all these Dipoles, they add up because they're going to be pointing in the it's a small exercise look at an alpha helix if you don't believe me So they have one Do you see the hydrogen pointing there? The blue part is nitrogen and the white hydrogen And then the next one there and the next one there and the next one there and the next one there So there are 3.6 of and there you see the The red oxygen and the green carbon. So all of these are pointing in the same direction from right to the left here And there's going to be one per amino acid So in a small helix like this there are probably 20 or so peptide bond dipoles and they all point in the same direction And what happens when you put many dipoles next to each other? Well, they add up so they form one much larger dipole that goes all the way from the right to the left so this helix This helix would have the same property as that there was a fairly large negative charge in the helix here And a fairly large positive charge in the entire helix there And you see this delta so that you can say delta minus there and plus delta there But if we now take a negatively charged residue and put it here They're going to love that because they pair up with the positive charge in the helix there And same thing there if we take a positively charged residue in particular arginine or lysine They're going to pair up with the negative charge here. So they effectively cap the helix So how can you use this? So doing this with physics would be difficult But this is implicitly what are your bioinformatics predictors do if you do the statistics If you have a helix and suddenly there is an aspartic acid It's likely that that marks the end of the helix and same thing is an arginine It's likely that if the region that we start to have an increasing fraction of helical residues And suddenly there is an arginine that is very likely the exact start of the helix And that's what our bioinformatics predictors find They're very good at finding these weak patterns And that is also related to the thing I showed you about the membrane proteins in the first lecture that the helixes can actually use this to Instead of having an aspartic or glutamic acid here This could be a pretty good interaction site for a negatively charged ion And the other side of the helix would be a good interacting site for a positively charged ion So the book sums up a bunch of these problems I so don't expect you to know all of these things about it But you need to know the important thing that I talked about because it's going to help you when you start looking at structures So we can start to look about What properties they have whether they have an NH group in the side chain Proline is the only odd one out there and then you can look in the side chain Do they have the C beta and how many heavier atoms do they have? And then you can start do they have a dipole? In case they are titratable, what is their pKa value? The pKa value is the value the pH value where we shift And here you see in particular histidine 6.5 Ugly close to 7 which means that it's hard to predict All the ones that say 4.3 or 10 or 12 or something they're going to be easy So if it's 4.3 or 3.9 Unless you're at very very low pa glue and as per going to be negatively charged and same thing with lysine and arginine Unless you're at an extremely high pa. They're going to be positively charged So do you ever have such low pa? You do and bacteria. So we have some of the iron channels we work with that's actually a channel that is pH regulated So it's usually open at pH 7. Sorry closed at pH 7 and opens at pH 4 So can you imagine a mechanism or something that would cause these channels to open or close? Amino acids changing their titration states That's because you can imagine that at very low pH You would have an amino acids that they are charged right and if they are now several amino acid with the same charge They're going to repel each other And now we change the pH so that they're suddenly neutral And then they don't repel each other anymore So nature tends to use this very simple physical properties to get things to move Same thing the movie about that channel I showed you before we're going to come back and talk more about membrane proteins later So why could it be good to have three charges on a helix? If you wanted to move or do something What happens when you put a charge in an electric field? There's a force on the charge and that force will lead to a motion So what electric fields do you have in your body? nerve signals They're tiny right? Roughly, what is the potential you have across a membrane in the cell? Yes, I would say to make to make life easy 80 is probably better but roughly 100 millivolts and it's actually lower on the inside of the cell So minus 100 millivolts on the inside of a cell. Is that a large or a small voltage? It's a Compared to battery. It's fairly low, right? But it's not the voltage that moves things. It's an electric field And the electric field is voltage divided over the distance by which you have the voltage drop What is the distance over which we have this voltage drop? 30 angstrom So suddenly the electric field we have in terms of voltage per meter is roughly 0.1 Divided by let's say 5 just to make it easier 5 times 10 to the minus 9 So the electric fields we have here It's like in the ballpark of 10 to the power of 9 volts per meter It's not even mega it's giga volts per meter Forget that the electric field here is far higher than the electric field you have around any of the high-tension wires out there There's an insanely high electric field in your nerve cells And then again what this table also should I think it's a good summary And of course, I expected to know this by heart tomorrow morning But you can also see here is that here you classify things This is common for have this just before an alpha helix Inside an alpha helix or the after an alpha helix in beta sheets or in loops or the core And you see that there are some patterns here, right? Some residues prefer starts of helices other prefers ends of helices or the inside Some residues much prefer be loops, but they don't like to be in helices Some of them prefer sheets, but hate helices and vice versa. So already here there are weak patterns And before we had so much sequence data We tried to understand and predict secondary structure based on these properties and it's worthless It's so much easier to do this based on homology today But overall amino acids occur in places where they stabilize that structure Which is not obvious But this goes back to Amphis and that structures are really determined by physical laws You could imagine the body designing and placing amino acids anywhere they want it But there is this some sort of reciprocity amino acids only occur in places where it's good to have that particular amino acid Which starts to touch upon the things that How do membrane how do proteins fold and when do they fold and what things can fold into a protein? Can do you think already now can any random sequence of amino acids fold into a protein? Do you have any idea how likely it is if I just create a random sequence of amino acids? Is it 50 50 or 1 in 10 or 1 in 100? We'll come back to that of course, but you're basically having a you basically have one chance in a billion It's virtually impossible to create a protein of random amino acids And why is an interesting question? I mentioned this a little bit when we spoke about beta sheets, but this is pretty cool Both beta sheets and helices can do something have something called a hydrophobic moment Just as I draw the dipole that you can think of a dipole as a moment from minus to plus to throw in the way the chart is Well, that is from minus to plus But the other difference is is that is our things charged or not charged And the same thing there you can create some sort of moment that says so what Do you have one side of a structure that is charged and another side of a structure that is not charged? So for a beta sheet Again, if we have this part with all the r-groups if we make all the lower side r-groups here hydrophobic And all the upper side r-groups here polar Then we effectively have one side of this sheet that is polar and the other one is hydrophobic That is a very different structure from you can imagine take exactly the same amino acids And they all prefer to be in beta sheets, but place them randomly in this sheet instead You have the same composition you have residues to prefer to be in sheet But let's say that I place them in periods of three or something or completely randomly You will likely still have exactly the same sheet, but the sheet as a whole is not going to have any net property It's going to be just as hydrophobic or hydrophilic on both sides You can use this you see the structure this section NMR structure And you see that because in NMR you get many different structures So that all these things are exempt from the structures Do you see that there's one sheet here that goes from say yellow to orange? And there's a second sheet that moves from blue to green or so And they're placed right on top of each other So what if you create something here that the outside here is hydrophilic and the inside is hydrophobic What you now just created is a small pocket right A small pocket that on the inside you can bind something that's hydrophobic But the pocket itself is hydrophilic and soluble in water And this is a FABP it stands for fatty acid binding protein So this is a protein that can transport fatty acids The fatty acids by themselves would not at all be soluble in your cell But we need to transport them to different points So you solubilize fatty acids on the inside of this protein But then the protein itself can move around and be quite soluble You can do something similar with an alpha helix, but it's a bit more complicated I like to say this call a helical wheel So first residue here one and then residue two and then residue three and then residue four So I just placed there is always hundred degrees between residues and an alpha helix So I just placed a space for the hundred degrees And in this case we're moving the helix is moving into the whiteboard And here too you can take residues that are completely happy to be an alpha helix and place them in random order But I don't think we have placed them in entirely random order here So you do see any difference between how things are placed here All the black ones They're hydrophobic and tryptophan is also quite hydrophobic And here you have polar things right and charged So you could probably imagine having this part be soluble in water And that part be on the inside of a protein You can probably even imagine two helixes like this binding to each other Because you don't tryptophan is bad because it's big and bulky But isolucine is a fairly small residue So we could have this black part team up with another similar black part on another helix And the two helixes would get reasonably close And let's see. I'm almost done here. So we're gonna finish on time I already touched upon this a bit, but this is basically just to sum up the whole point that The reason why I don't call them charged residues is that they might not really be charged If I move beyond pH 4 The glue and asp might not really be charged anymore, but they can be charged on a specific pH Same thing with lysine and arginine The one thing to keep in mind here is histidine Because histidine will change its protonation depending on the surrounding The problem is that it's not just going to matter on the pH You could imagine based on the pH of 6.5 Well, then you could argue that histidine should maybe if you're Based based the titration state exactly on the pH There's one more complication in histidine that we have two sites where you can be protonated But the problem is that what if you have an oxygen right next to the histidine? Then it's likely going to be more favorable To have a hydrogen in that position on the histidine On the other hand if we take this histidine and put it right in the middle of a protein Where there are no partners Then it's likely going to be less favorable to have a hydrogen there So these pka values they are the ones you have for an isolated amino acid out of your water But what happens inside proteins are things will shift around a bit and it's even called pka shifts Which we're not going to go through in this course, but you can these are guidelines But you can't trust them absolutely It will depend So how do we determine whether a histidine is charged or not? With great difficulty We pretty much can't And it's an outstanding gigantic problem just trying to calculate pka shifts is also extremely difficult So having good predictors of pka shift is one of the big outstanding computational biome We I so wish I had an elsewhere, but I don't Once you have a structure we can usually cheat because if again, I can't see the hydrogens in an x-ray structure There are too few electrons in them But if I see that there is a big oxygen right next to it I'm going to say ah the hydrogen is on the left side of this histidine Which is of course a guess I could be wrong there, but in general we're not But in general it's a problem that we haven't solved yet And I already mentioned that. Oh, sorry. There we have it there. We have it. Ah, you see that we have a A delta nitrogen and an epsilon nitrogen in this ring So that we can choose to either protonate that side or protonate that side or protonate both of them So normally you would have either the delta or the epsilon protonated and then it's neutral Or you have both of them protonated and then it's charged to make life even more difficult for you. Sorry This doesn't happen at exactly a specific pH because this too is determined by the Boltzmann distribution, right? So as you go through a pH change here, you're going to start out from having something be 100% protonated And then the probability gradually decreases. So suddenly you're 90, 80, 50, 10 eventually and then at some pH You're so low so that you can start to assume that after this pH, it's not protonated at all anymore And how broad this range is varies, but it's usually in the bulk of one pH unit Which makes it even more difficult for histidine, right? Because that if we are somewhere here It's not just a matter of determining whether it's protonated or not protonated. It can be 30% protonated How on earth can something be 30% protonated? Yes, or as a function of that things exchange over time, right? So that the proton will somehow it will bind a proton and then release a proton and then binds a proton again Then releases a proton again And the reason is I so wish I didn't have to torment you with this But the reason why this is important is that it's so related binding charged molecules protein stability iron channels opening DNA protein interactions are determined by charges because you have all those charts phosphates and the proteins that Electrostatic interactions are super strong and when they occur they tend to determine everything we know about that particular case And that's of course why so many very very large and famous research groups have spent decades trying to get better at predicting pK Values we are far better today than we were 20 30 years ago, but it's still not a solved problem And we cancel with bioinformatics Oh, I even have my pet channel here. So this is ha ha You might start to see a pattern that I tend to talk about the molecules we do research on So this is what the channel looks at at low pH. Do you see that how things are pretty much repelling each other? And then what happens when you make a p and normally then you make a pH jump and what will eventually happen Is that when this helices get closer together The thin pore here is going to become so narrow that this water channel here breaks And then it can't conduct ions anymore and at some point it's going to be entirely packed and then the whole the pore here is closed And that is based on titration states of residues We think The problem is that we haven't the problem there are lots of titratable residues in this channel something like 20 of them And we know that if we change all of them we can force it to open or close We still haven't been able to identify one single residue that explains all of it So this far nature is smarter than we have been Ah, we can even see it closing there. Look at the middle there. You're going to start to see that it Breaks the water channel shortly Do you see there now that in this part here that there are two rings here of hydrophobic residues And you see now there is no water anymore. And when there is no water here, it will not be able to conduct ions So now it has actually closed And this takes I think two three microseconds is still a very fast process. Many of them are much slower Good. And I think that's uh Brings us to the end of today This is mostly chapters seven and ten skip chapters eight and nine for now Because that's going to be a bit of the physics that I think we'll talk about tomorrow And what you need to understand of this is Compare this with the first lecture the difference now is that now we need to understand the secondary structure in terms of enthalpy and entropy And we need to just under not just say that oh, some things are More frequent in some places, but you need to understand why is that that polians don't like alpha helices and why is it that glycine doesn't like alpha helices And I think either tomorrow or it might be after break We're actually going to start thinking a little bit more about exactly how the secondary structure elements form Because we can learn a lot about their formation From the very simple f equals e minus ts equations And then I have a bunch of questions that we're going to go through tomorrow morning But before that you're going to have a lab this afternoon Enjoy it and then we for wednesday we decided that while darry can't be around björn and I will take that lab So there are no changes in any of the schedules So lab this afternoon and then we'll meet tomorrow again. Good to see you